Abstract : A study has been made of the oscillations in a one-dimensional nonuniform plasma bounded by specularly reflecting walls. The nonuniformity is assumed to arise from a parabolic shaped static potential distribution. Static magnetic fields and longitudinal propagation are not included. Using Maxwell's equations and the linearized Boltzmann-Vlasov equation, a linear integral equation is derived. This equation is solved numerically to yield the resonances and damping rates of the various modes of the plasma. An alternative solution is obtained by using pressure theory. Comparison of results obtained by both methods shows good agreement, in contrast to earlier results for an infinite plasma, for which the agreement was poor. (Author)